Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Variance enhancement”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Subgrid-scale horizontal and vertical variation of cloud water in stratocumulus clouds: a case study based on LES and comparisons with in situ observations

Abstract. Stratocumulus clouds in the marine boundary layer cover a large fraction of ocean surface and play an important role in the radiative energy balance of the Earth system. Simulating these clouds in Earth system models (ESMs) has proven to be extremely challenging, in part because cloud microphysical processes such as the autoconversion of cloud water into precipitation occur at scales much smaller than typical ESM grid sizes. An accurate autoconversion parameterization needs to account for not only the local microphysical process (e.g., the dependence on cloud water content qc and cloud droplet number concentration Nc) but also the subgrid-scale variability of the cloud properties that determine the process rate. Accounting for subgrid-scale variability is often achieved by the introduction of a so-called enhancement factor E. Previous studies of E for autoconversion have focused more on its dependence on cloud regime and ESM grid size, but they have largely overlooked the vertical dependence of E within the cloud. In this study, we use a large-eddy simulation (LES) model, initialized and constrained with in situ and surface-based measurements from a recent airborne field campaign, to characterize the vertical dependence of the horizontal variation of qc in stratocumulus clouds and the implications for E. Similar to our recent observational study (Zhang et al., 2021), we found that the inverse relative variance of qc, an index of horizontal homogeneity, generally increases from cloud base upward through the lower two-thirds of the cloud and then decreases in the uppermost one-third of the cloud. As a result, E decreases from cloud base upward and then increases towards the cloud top. We apply a decomposition analysis to the LES cloud water field to understand the relative roles of the mean and variances of qc in determining the vertical dependence of E. Our analysis reveals that the vertical dependence of the horizontal qc variability and enhancement factor E is a combined result of condensational growth throughout the lower portion of the cloud and entrainment mixing at cloud top. The findings of this study indicate that a vertically dependent E should be used in ESM autoconversion parameterizations.

54 ENVIRONMENTAL SCIENCES↗

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

A Model Study of the Relative Influences of Scavenging and Circulation on 230Th and 231Pa in the Western North Atlantic

The oceanic cycles of thorium-230 and protactinium-231 are affected by a number of processes, such as removal by adsorption to settling particles and transport by ocean currents. Measurements obtained as part of GEOTRACES and earlier programs have shown that, in the North Atlantic, the activities of dissolved 230Th (230Thd) and 231Pa (231Pad) at abyssal depths are lower near the western margin than in the basin interior. At least two factors could explain the lower 230Thd and 231Pad near the margin: (i) intensified scavenging in benthic nepheloid layers (BNLs) extending a thousand meters or more above the seafloor; and (ii) ventilation by relatively 230Thd- and 231Pad-poor waters emanating from the Deep Western Boundary Current (DWBC).Here a regional ocean circulation model with ?eddy-permitting' resolution (1/4) that incorporates 230Th and 231Pa is used in an effort to reproduce the observed distributions of 230Th and 231Pa in the western North Atlantic. In this model, 230Th and 231Pa removal from solution is governed by a prescribed distribution of particulate matter that is derived from a recent synthesis of nephelometer and transmissometer data. The model simulates a meandering Gulf Stream and a DWBC along the continental slope and rise, although noticeable differences with physical observations also exist. A model solution is found that explains most of the variance of 230Thd measurements (85%) and 231Pad measurements (81%) from (pre-)GEOTRACES cruises. On the other hand, measurements of particulate 230Th (230Thp) and 231Pa (231Pap) are more difficult to reproduce, with the same solution accounting for only 49% (11%) of the 230Thp (231Pap) variance. Sensitivity experiments suggest that the low 230Thd and 231Pad activities observed near the western margin are due to enhanced removal rates of both nuclides in BNLs rather than to deep water ventilation from the western boundary. The radionuclide activities present in the DWBC at its inflow location are also found to strongly influence the basin-scale distributions of 230Th and 231Pa. Overall, our study points to BNLs as important sites of 230Th and 231Pa scavenging in the ocean and illustrates the difficulty to explain simultaneously radionuclide measurements in dissolved and particulate forms in the studied area.

Lerner, Paul↗

A Bayesian inferencing framework for ultrasound wave speed measurements in metal additive manufacturing

Process-related changes during metal additive manufacturing introduce microstructural variability in the material properties of printed parts, directly affecting component reliability. Accurate estimation of these property variations with part performance are essential for quality assurance. Ultrasound testing offers a non-destructive means to estimate mechanical properties and detect defects; however, conventional analysis methods often neglect the influence of microstructural variability, limiting their effectiveness. Here, this research presents a Bayesian inference technique for quantifying wave speed uncertainty from ultrasound measurements of metal additive manufactured parts. By integrating prior ultrasound data with a Bayesian model, the proposed approach generates posterior density estimates of wave speed that systematically account for manufacturing-induced variability and uncertainty. The novelty of this research lies in applying a Bayesian framework to analyze experimental ultrasound measurements within the context of metal additive manufacturing variability. The method enhances the accuracy of wave speed estimation by 64%, defect position by 50% and increases confidence associated with wave speed variance by 30% across different porosity levels, thereby providing a robust foundation for improved decision-making and increased reliability in additively manufactured components.

Additive manufacturing↗

Radar image processing for rock-type discrimination

Image processing and enhancement techniques for improving the geologic utility of digital satellite radar images are reviewed. Preprocessing techniques such as mean and variance correction on a range or azimuth line by line basis to provide uniformly illuminated swaths, median value filtering for four-look imagery to eliminate speckle, and geometric rectification using a priori elevation data. Examples are presented of application of preprocessing methods to Seasat and Landsat data, and Seasat SAR imagery was coregistered with Landsat imagery to form composite scenes. A polynomial was developed to distort the radar picture to fit the Landsat image of a 90 x 90 km sq grid, using Landsat color ratios with Seasat intensities. Subsequent linear discrimination analysis was employed to discriminate rock types from known areas. Seasat additions to the Landsat data improved rock identification by 7%.

Blom, R. G.↗

Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.

Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.

61 RADIATION PROTECTION AND DOSIMETRY↗

Impact of lossy compression on diagnostic accuracy of radiographs for periapical lesions

OBJECTIVES: The purpose of this study was to evaluate the lossy Joint Photographic Experts Group compression for endodontic pretreatment digital radiographs. STUDY DESIGN: Fifty clinical charge-coupled device-based, digital radiographs depicting periapical areas were selected. Each image was compressed at 2, 4, 8, 16, 32, 48, and 64 compression ratios. One root per image was marked for examination. Images were randomized and viewed by four clinical observers under standardized viewing conditions. Each observer read the image set three times, with at least two weeks between each reading. Three pre-selected sites per image (mesial, distal, apical) were scored on a five-scale score confidence scale. A panel of three examiners scored the uncompressed images, with a consensus score for each site. The consensus score was used as the baseline for assessing the impact of lossy compression on the diagnostic values of images. The mean absolute error between consensus and observer scores was computed for each observer, site, and reading session. RESULTS: Balanced one-way analysis of variance for all observers indicated that for compression ratios 48 and 64, there was significant difference between mean absolute error of uncompressed and compressed images (P <.05). After converting the five-scale score to two-level diagnostic values, the diagnostic accuracy was strongly correlated (R (2) = 0.91) with the compression ratio. CONCLUSION: The results of this study suggest that high compression ratios can have a severe impact on the diagnostic quality of the digital radiographs for detection of periapical lesions.

NASA Discipline Space Human Factors↗

On the Regulation of the Pacific Warm Pool Temperature

In the tropical western Pacific, regions of the highest sea surface temperature (SST) and the largest cloud cover are found to have the largest surface heating, primarily due to the weak evaporative cooling associated with weak winds. This situation is in variance with the suggestions that the temperature in the Pacific warm pool is regulated either by the reduced solar heating due to an enhanced cloudiness or by the enhanced evaporative cooling due to an elevated SST. It is clear that an enhanced surface heating in an enhanced convection region is not sustainable and must be interrupted by variations in large-scale atmospheric circulation. As the deep convective regions shift away from regions of high SST due primarily to seasonal variation and secondarily to interannual variation of the large-scale atmospheric and oceanic circulation, both trade wind and evaporative cooling in the high SST region increase, leading to a reduction in SST. We conclude that the evaporative cooling associated with the seasonal and interannual variations of trade winds in the primary factor that prevent the warm pool SST from increasing to a value much higher than what is observed.

Chou, Ming-Dah↗

Exploratory Analysis of Carbon Dioxide Levels, Ultrasound and Optical Coherence Tomography Measures of the Eye During ISS Missions

Enhanced screening for the Visual Impairment/Intracranial Pressure (VIIP) syndrome has been implemented to better characterize the ocular and vision changes observed in some long-duration crewmembers. This includes implementation of in-flight ultrasound in 2010 and optical coherence tomography (OCT) in 2013. Potential risk factors for VIIP include cardiovascular health, diet, anatomical and genetic factors, and environmental conditions. Carbon dioxide (CO2), a potent vasodilator, is chronically elevated on the International Space Station (ISS) relative to ambient levels on Earth, and is a plausible risk factor for VIIP. In an effort to understand the possible associations between CO2 and VIIP, this study explores the relationship of ambient CO2 levels on ISS compared to inflight ultrasound and OCT measures of the eye obtained from ISS crewmembers. CO2 measurements were aggregated from Operational Data Reduction Complex and Node 3 major constituent analyzers (MCAs) on ISS or from sensors located in the European Columbus module, as available. CO2 levels in the periods between each ultrasound and OCT session are summarized using timeseries metrics, including time-weighted means and variances. Partial least squares regression analyses are used to quantify the complex relationship between specific ultrasound and OCT measures and the CO2 metrics simulataneously. These analyses will enhance our understanding of the possible associations between CO2 levels and structural changes to the eye which will in turn inform future analysis of inflight VIIP data.

Schaefer, C.↗

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach

The time evolution of particle number fluctuations in nuclear collisions at intermediate energies (E lab = 1.23–10⁢A GeV) is studied by means of the UrQMD-3.5 transport model. The transport description incorporates baryonic interactions through a density-dependent potential. This allows for an implementation of a first-order phase transition including a mechanically unstable region at large baryon density. The scaled variance of the baryon and proton number distributions is calculated in the central cubic spatial volume of the collisions at different times. A significant enhancement of fluctuations associated with the unstable region is observed. This enhancement persists to late times, reflecting a memory effect for the fluctuations. The presence of the phase transition has a much smaller influence on the observable event-by-event fluctuations of protons in momentum space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Representing methane emissions from wet tropical forest soils using microbial functional groups constrained by soil diffusivity

Tropical ecosystems contribute significantly to global emissions of methane (CH 4 ), and landscape topography influences the rate of CH 4 emissions from wet tropical forest soils. However, extreme events such as drought can alter normal topographic patterns of emissions. Here we explain the dynamics of CH 4 emissions during normal and drought conditions across a catena in the Luquillo Experimental Forest, Puerto Rico. Valley soils served as the major source of CH 4 emissions in a normal precipitation year (2016), but drought recovery in 2015 resulted in dramatic pulses in CH 4 emissions from all topographic positions. Geochemical parameters including (i) dissolved organic carbon (C), acetate, and soil pH and (ii) hydrological parameters like soil moisture and oxygen (O 2 ) concentrations varied across the catena. During the drought, soil moisture decreased in the slope and ridge, and O 2 concentrations increased in the valley. We simulated the dynamics of CH 4 emissions with the Microbial Model for Methane Dynamics-Dual Arrhenius and Michaelis–Menten (M3D-DAMM), which couples a microbial functional group CH 4 model with a diffusivity module for solute and gas transport within soil microsites. Contrasting patterns of soil moisture, O 2 , acetate, and associated changes in soil pH with topography regulated simulated CH 4 emissions, but emissions were also altered by rate-limited diffusion in soil microsites. Changes in simulated available substrate for CH 4 production (acetate, CO 2 , and H 2 ) and oxidation (O 2 and CH 4 ) increased the predicted biomass of methanotrophs during the drought event and methanogens during drought recovery, which in turn affected net emissions of CH 4 . A variance-based sensitivity analysis suggested that parameters related to aceticlastic methanogenesis and methanotrophy were most critical to simulate net CH 4 emissions. This study enhanced the predictive capability for CH 4 emissions associated with complex topography and drought in wet tropical forest soils.

54 ENVIRONMENTAL SCIENCES↗

Wind Profiles Derived from Volume Imaging Lidar Data: Enhancements to the Algorithm and Comparisons with Insitu Observations

This paper presents wind measurements made with the University of Wisconsin Volume Imaging Lidar (VIL) during Aug. 1989 as part of the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE). Enhancements to the algorithm are described. Comparisons of these results to aircraft, balloon, and surface based wind measurements are presented. Observations of the spatial variance of aerosol backscatter are also compared to measurements of the convective boundary layer depth. Measurements are based on two-dimensional cross correlations between horizontal image planes showing the spatial distribution of aerosol scattering observed by the lidar at intervals of approximately 3 minutes. Each image plane covers an area of 500-1000 sq km and the winds calculated represent area averages.

Piironen, A. K.↗

The Impacts of Freshwater Input and Surface Wind Velocity on the Strength and Extent of a Large High Latitude River Plume

Arctic Ocean physical and biogeochemical properties are strongly influenced by freshwater input from land and through the Bering Strait, where the mean currents transport water northward from the Bering Sea. The Yukon River is one of the largest rivers in North America and the Arctic, contributing large quantities of freshwater and terrigenous material to the coastal ocean in the northern Bering Sea. However, a detailed analysis of the coastal hydrodynamics at the outflow of the river has not been conducted in this remote but regionally important river. A three-dimensional hydrodynamic model was built to represent the lower Yukon River and coastal ocean for the ice-free months in 7 years. On average, a large anticyclonic eddy persisted at the main outflow of the Yukon that recirculates water back toward the coast where the currents converge to form a mean northward transport along the delta. Interannual spatial variance in salinity was relatively small, while there was substantial variance in u and v current velocity. u velocity spatial variance was correlated to the volume of freshwater discharge across years, while v velocity spatial variance was correlated to the N–S wind velocity. During strong wind events, plume structure was substantially altered: southerly winds deepened the plume and enhanced northward transport, while northerly winds shoaled and strengthened the pycnocline, and reversed the flow toward the south. The variability in plume dispersion on short time scales due to wind forcing has implications for where terrigenous material is processed in and settles out of the water column.

river plume↗

Resolved gravity waves in the tropical stratosphere: Impact of horizontal resolution and deep convection parametrization

Convectively generated gravity waves (CGGWs) are important for numerical weather prediction due to their effect on the quasi-biennial oscillation (QBO) in the stratosphere. Here, using global ECMWF IFS simulations at TCo7999 (or 1.25 km), TCo2559 (or 3.9 km) and TCo1279 (or 7.8 km) horizontal resolutions, sensitivity of resolved CGGWs to the horizontal resolution and to the explicit versus parametrized representation of deep convection is elucidated during the westerly shear phase of the QBO. Parametrized deep convection is found to inhibit CGGWs, resulting in a twofold reduction in CGGW forcing. When deep convection is explicitly resolved, the total CGGW forcing is almost unchanged across the horizontal resolutions. However, the contribution of long and mesoscale CGGWs (with horizontal wavelengths 100 km ≤ $λ_h$ < $1,900$ km) to the total CGGW forcing decreases and the contribution of smaller-scale CGGWs (with $λ_h$ < $100$ km) increases as the horizontal resolution increases. At the maximum CGGW forcing altitude, at TCo7999 resolution 43% of the total CGGW forcing is due to long and mesoscale waves, whereas at TCo2559 and TCo1279 resolutions their contribution is 70% and 90%, respectively. While CGGW forcing from long and mesoscale waves is similar at TCo7999 resolution with explicit deep convection and at TCo1279 resolution with parametrized deep convection, CGGW forcing from these waves is artificially enhanced at TCo1279 and TCo2559 resolutions with explicit deep convection. This is due to the explicit deep convection being too strong and having too much variance for 100 km ≤ $λ_h$ < $1,900$ km. Therefore, parametrizations of deep convection and CGGWs (to account for forcing from waves with $λ_h$ < $100$ km) are required even at TCo2559 resolution. Additionally, resolved CGGW forcing at TCo7999 resolution is examined for the easterly shear phase of the QBO; similar to the westerly shear phase, the smaller-scale waves contribute 55% to the total CGGW forcing at the maximum CGGW forcing altitude.

54 ENVIRONMENTAL SCIENCES↗

Photon number resolving detection with a single-photon detector and adaptive storage loop

Abstract Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.

Sullivan, Nicholas M. (ORCID:0000000248447296)↗

A temporal analysis and response to nitrate availability of 3D root system architecture in diverse pennycress (Thlaspi arvense L.) accessions

Introduction Roots have a central role in plant resource capture and are the interface between the plant and the soil that affect multiple ecosystem processes. Field pennycress ( Thlaspi arvense L.) is a diploid annual cover crop species that has potential utility for reducing soil erosion and nutrient losses; and has rich seeds (30-35% oil) amenable to biofuel production and as a protein animal feed. The objective of this research was to (1) precisely characterize root system architecture and development, (2) understand plastic responses of pennycress roots to nitrate nutrition, (3) and determine genotypic variance available in root development and nitrate plasticity. Methods Using a root imaging and analysis pipeline, the 4D architecture of the pennycress root system was characterized under four nitrate regimes, ranging from zero to high nitrate concentrations. These measurements were taken at four time points (days 5, 9, 13, and 17 after sowing). Results Significant nitrate condition response and genotype interactions were identified for many root traits, with the greatest impact observed on lateral root traits. In trace nitrate conditions, a greater lateral root count, length, density, and a steeper lateral root angle was observed compared to high nitrate conditions. Additionally, genotype-by-nitrate condition interaction was observed for root width, width:depth ratio, mean lateral root length, and lateral root density. Discussion These findings illustrate root trait variance among pennycress accessions. These traits could serve as targets for breeding programs aimed at developing improved cover crops that are responsive to nitrate, leading to enhanced productivity, resilience, and ecosystem service.

59 BASIC BIOLOGICAL SCIENCES↗

Robust Optimized Pulse Schemes for Atomic Fountain Interferometry

The robustness of an atomic fountain interferometer with respect to variations in the initial velocity of the atoms and deviations from the optimal pulse amplitude is examined. We numerically simulate the dynamics of an interferometer in momentum space with a maximum separation of and map out the expected signal contrast depending on the variance of the initial velocity distribution and the value of the laser field amplitude. We show that an excitation scheme based on rapid adiabatic passage significantly enhances the expected signal contrast, compared to the commonly used scheme consisting of a series of and pulses. We demonstrate further substantial increase of the robustness by using optimal control theory to identify splitting and swapping pulses that perform well on an ensemble average of pulse amplitudes and velocities. Our results demonstrate the ability of optimal control to significantly enhance future implementations of atomic fountain interferometry.

74 ATOMIC AND MOLECULAR PHYSICS↗